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GATE 2025 IN – Question 37

Engineering Mathematics · Numerical methods · 2 marks · Multiple choice

Newton-Raphson method is used to compute the inverse of the number 1.6. Among the following options, the initial guess of the solution that results in non-convergence of the iterative process is

  1. 0.55
  2. 0.75
  3. 1.15
  4. 1.25

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Correct answer: (D) 1.25

Explanation

Applying Newton to 1/x−1.6=0 gives xn+1=xn(2−1.6xn).

Convergence to the positive reciprocal requires |1−1.6x0|<1.

At x0=1.25 the next iterate is zero, where the original reciprocal function is undefined; the iteration cannot converge to 0.625.

Therefore **D**.